Eric Lasley

University of Massachusetts Amherst

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Trends

Author Order

Document Type

Co-Authors

Peter Carruthers

University of Maryland, College Park

Eugene Golowich

University of Massachusetts Amherst

V. Kapila

University of Massachusetts Amherst

Cooperative Institutions

University of Massachusetts Amherst

University of Maryland, College Park

University of Stirling

City, University of London

University of Kent

Google (United States)

Pontifical Catholic University of Peru

University of Sheffield

Bridge University

Cambridge University Press

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Field

Reactionωπ→ωπin the Veneziano Model

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (1970)

Peter Carruthers Eric Lasley

A set of invariant amplitudes for the reaction $\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$ is constructed within the framework of the Veneziano model by expansions of the form $\ensuremath{\Sigma}(\mathrm{polynomials})\ifmmode\times\else\texttimes\fi{}(\mathrm{beta}\mathrm{function})$. The dominant asymptotic behavior corresponds to the $f$ trajectory in the $t$ channel and the $\ensuremath{\rho}$ and $B$ trajectories in the $s$ and $u$ channels. Separate treatments are given for the $\ensuremath{\rho}$ and $B$ contributions. In every case the leading trajectory poles have correct spin-parity as a consequence of enforcing proper asymptotic behavior on the invariant amplitudes. These relations are nontrivial and differ for the $\ensuremath{\rho}$ and $B$ contributions. The detailed construction of the amplitudes for $\ensuremath{\omega}\ensuremath{\pi}$ scattering differs from most previous applications because of the absence of an exotic channel. $\ensuremath{\omega}\ensuremath{\pi}$ scattering is notable in the number of terms required to represent the amplitude; a 72-parameter amplitude built using ${B}_{11}$, ${B}_{12}$, and ${B}_{21}$ cannot satisfy simple physical requirements for the $\ensuremath{\rho}$ trajectory. One must add further terms lacking the $\ensuremath{\rho}$ pole (such as ${B}_{22}$) in order to avoid decoupling the $\ensuremath{\rho}$ trajectory. The $B$ contribution is easily treated in direct analogy to the $\ensuremath{\rho}$ trajectory in $A\ensuremath{\pi}$ scattering. The implication of the hypothesis of partially conserved axial-vector current (PCAC) that the invariant amplitude ${T}_{1}$ (coefficient of ${e}^{\ensuremath{'}}\ifmmode\cdot\else\textperiodcentered\fi{}e$) should vanish at the Adler point is somewhat delicate because of the near degeneracy of the $\ensuremath{\omega}$ and $\ensuremath{\rho}$ mesons. The signature and amplitude conspiracy relations ensure the suppression of the apparent pole.

10.1103/physrevd.1.1204

Cite

Citations (6)

Current Algebra and the Trace of the Energy-Momentum Tensor

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (1971)

Eugene Golowich Eric Lasley

We consider a model in which the trace of the energy-momentum tensor, $\ensuremath{\Theta}\ensuremath{\equiv}{{\ensuremath{\Theta}}^{\ensuremath{\mu}}}_{\ensuremath{\mu}}$, contains both $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$-invariant and -breaking terms. The latter are assumed to be proportional to ${S}_{0}$ and ${S}_{8}$, the $T=0$, ${J}^{P}={0}^{+}$ members of $(3,{3}^{*})\ensuremath{\bigoplus}({3}^{*},3)$. Each contribution to the trace is weighted by four minus the dimension of the associated local-field operator. Using Jacobi identity relations, we prove that the dimensions of ${S}_{0}$ and ${S}_{8}$ are equal. In order to investigate the consequences of the assumed chiral properties of the energy-momentum trace, we examine the $\ensuremath{\pi}\ensuremath{\pi}$, $\ensuremath{\pi}{A}_{1}$, and ${A}_{1}{A}_{1}$ matrix elements of $\ensuremath{\Theta}$. Ward-identity relations are employed to constrain the off-shell extensions of these matrix elements. In our model, the dimension $d$ of ${S}_{0}$ and ${S}_{8}$ is found to equal two in the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ limit of massless pions. We also derive a more general relation for $d$ valid even when $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ is only an approximate symmetry. Scalar-dominance and smoothness assumptions enable us to extract additional information from this model. We predict $\frac{\ensuremath{\Gamma}({A}_{1}\ensuremath{\rightarrow}\ensuremath{\epsilon}\ensuremath{\pi})}{\ensuremath{\Gamma}(\ensuremath{\epsilon}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi})}=0.07$ for the ${A}_{1}(1070)$ and $\ensuremath{\epsilon}(700)$ partial widths. Our model also leads to tentative conclusions concerning two subjects of current interest: the possibility that scalar mesons couple to $\ensuremath{\Theta}$ with a universal strength, and the existence of chiral-invariant contributions to $\ensuremath{\Theta}$.

TRACE (psycholinguistics)

10.1103/physrevd.3.3114

Cite

Citations (2)

MINIMAL FACTORIZED VENEZIANO AMPLITUDES FOR THE REACTIONS A$sub 1$$pi$ $Yields$ A$sub 1$$pi$, A$sub 1$$pi$ $Yields$ $pi$$pi$, $pi$$pi$ $Yields$ $pi$.

Eric Lasley Peter Carruthers

Pi interaction

Source

Cite

Citations (0)

Minimal Factorized Veneziano Amplitudes for the ReactionsA1π→A1π,

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (1970)

Eric Lasley Peter Carruthers

Explicit minimal amplitudes are constructed for the reactions ${A}_{1}\ensuremath{\pi}\ensuremath{\rightarrow}{A}_{1}\ensuremath{\pi}$, ${A}_{1}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$, and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$. All amplitudes have correct Regge asymptotic behavior corresponding to the (degenerate) $\ensuremath{\rho}\ensuremath{-}f$ trajectory dominant in all channels. Signature is systematically enforced to leading order so that the poles on the leading trajectory have the correct spin and parity. The parity-conserving helicity amplitudes for ${A}_{1}\ensuremath{\pi}\ensuremath{\rightarrow}{A}_{1}\ensuremath{\pi}$ factorize, and multichannel factorization for the three coupled amplitudes is enforced for the leading trajectory. Multichannel factorization requires the extension of the ${A}_{1}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ amplitude, but the parameters in the new amplitude are all determined, except for two which can be identified with the (independent) ${A}_{1}\ensuremath{\rho}\ensuremath{\pi}$ couplings ${G}_{S}$ and ${G}_{D}$. Two acceptable ${A}_{1}\ensuremath{\pi}\ensuremath{\rightarrow}{A}_{1}\ensuremath{\pi}$ amplitudes are found, each involving two arbitrary constants in addition to ${f}_{\ensuremath{\rho}}={f}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}, {G}_{S}, {G}_{D}$, and the three ${A}_{1}{A}_{1}\ensuremath{\rho}$ couplings ${g}_{1}$, ${g}_{2}$, and ${g}_{3}$. These couplings are not constrained by the model except for one relation connecting ${G}_{D}$ and ${g}_{3}$. These results are compared with the hard-pion analysis by Schnitzer and Weinberg.

Helicity

10.1103/physrevd.2.1724

Cite

Citations (1)

Aspects of the Scalar-Dominance Hypothesis

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (1971)

Eugene Golowich Eric Lasley V. Kapila

The scalar-dominance hypothesis, incorporating $\ensuremath{\epsilon}(700)\ensuremath{-}{\ensuremath{\epsilon}}^{\ensuremath{'}}(1060)$ mixing, is applied to a large class of elastic, single-particle matrix elements of the energy-momentum trace operator.

Dominance (genetics)

10.1103/physrevd.4.2070

Cite

Citations (4)